In this article we carried out a comprehensive investigation of true minima on the potential energy surface (PES) for the alpha-cyclodextrin molecule using ab initio Hartree-Fock (HF) and density functional theory (DFT) quantum chemical methods, employing basis sets ranging from 6-31 G(d,p) to 6-311++G(2d,2p) triple-zeta quality. Thermodynamic quantities and the solvent effect were evaluated at the DFT level of theory. We believe that the most relevant conformers present on the multidimensional PES were sampled in our work, using an adequate treatment of electron correlation effects to describe the intramolecular hydrogen bonds that are present in cyclodextrin species. We present new structures not reported so far and discuss, in detail, the relevance of the DFT gas-phase equilibrium structures for the experimental and theoretical studies involving cyclodextrins and corresponding inclusion complexes, in the condensed phase. In addition, among the various true minimum energy structures located on the DFT PES, the preferred structures in the gas phase and aqueous media, needed to be used as representative minima on the PES in further studies involving the interaction of alpha-cyclodextrin with other species, were unambiguously identified.